Exploring Proportional Relationships through Tables and Equations

The video tutorial explains how to find the constant of proportionality from a table and express it as an equation. It introduces a strategy to understand proportional relationships, emphasizing that they start at the origin. The tutorial uses a job analogy to relate X and Y values to hours worked and money earned, leading to the creation of an equation. Key vocabulary such as input, output, unit rate, and slope are discussed, along with graphing concepts. The video also addresses handling non-standard increments in tables.

What is the first step in understanding a proportional relationship?

• Identify the slope

• Check if it starts at the origin

• Find the y-intercept

• Calculate the unit rate

In the given table, what does the ordered pair (0, 0) signify?

• The unit rate

• The slope of the line

• The maximum value of y

• The starting point of the relationship

If you work 3 hours, how much money will you have earned according to the table?

• $75

• $45

• $60

• $30

What is the equation for the proportional relationship described in the video?

• y = 15x

• y = 15 + x

• y = 15x + 1

• y = x + 15

What does the variable 'x' represent in the equation y = 15x?

• Unit rate

• Number of hours worked

• Starting amount

• Total amount of money

What is the term for the number that we put into our equation?

• Unit rate

• Input

• Slope

• Output

What does the term 'unit rate' refer to in the context of the video?

• The total amount of money

• The number of hours worked

• The amount of money earned per hour

• The starting amount

How is the slope related to the unit rate in a graph?

• It represents the rate of change

• It is the x-intercept

• It indicates the total amount of money

• It shows the starting point

If the hours worked are not counted by ones, how do you calculate the unit rate?

• Divide the change in y by the change in x

• Add the change in y to the change in x

• Multiply the change in y by the change in x

• Subtract the change in x from the change in y

In the example where hours increase by 2, what is the unit rate if the money increases by $8?

• $16 per hour

• $2 per hour

• $4 per hour

• $8 per hour